Digital Signal Processing Reference
In-Depth Information
Our bandpass filter is - in a physical sense - a simple resonant circuit which can practi-
cally only resonate with one frequency. Like a children's swing. Once it has been set in
motion it swings with only one frequency, its natural frequency f
E
. If it is pushed regularly
- periodically - it will only reach the maximum swing when this occurs precisely in the
rhythm of its natural frequency. The second series in Illustration 122 shows this case.
If the rhythm of the energy supply gets somewhat bigger or smaller, cause and effect are
in certain moments in phase, then less and less until they are contra-phase. In this case the
swing would be given a push when it approaches the person pushing and slowed down
here. “In phase” is equivalent to the case in which the swing is pushed in the direction of
motion. The deflection is then temporarily greatest.
In the three bottom cases in Illustration 122 the “swing” bandpass filter is given a push at
times in the right or at least almost right rhythm and then in the wrong rhythm. The
deflection increases or decreases in a certain rhythm. Experts call this the beat frequency
f
B
. This is reproduced by the envelope.
The following result should be noted: even when a sinusoidal voltage is switched on the
reaction of the resonant circuit reveals the process which takes place physically within it.
It tries to oscillate with its natural frequency. At the beginning it swings like a swing with
its natural frequency if the activating frequency differs slightly. The more the activating
frequency differs
temporarily
from the natural frequency the more weakly the resonant
circuit resonates in the stationary state.
The bottom part of Illustration 122 shows this very clearly. It shows the four transients in
the frequency domain. The peaks in the spectrum represent the
input signals
activating the
bandpass (100, 104, 108, 116 Hz). The remaining spectrum derives from the bandpass/
resonant circuit and occurs mainly at 100Hz (
natural frequency
).
